论文标题
统一群体的全球gan-gross-prosad猜想：内窥镜病例
The global Gan-Gross-Prasad conjecture for unitary groups: the endoscopic case
论文作者
论文摘要
在本文中，我们证明了在所有内窥镜病例中，我们证明了gan-gross-prosad的猜想和统一组$ u_n \ times u_ {n+1} $的Ichino-ikeda猜想。我们的主要技术创新是计算某些Cuspidal数据的贡献，称为$*$ - 通用，对线性组的Jacquet-Rallis Trace公式。我们提供了两种不同的贡献计算：一个基于截断的基于Eisenstein系列的Rankin-Selberg时期和Flicker-Rallis交织期。另一个建立在Zeta积分的基础上，用惠特克模型上的功能表示。还给出了两个表达式之间平等的直接证明。最后，提供了有关Jacquet-Rallis痕量公式的光谱膨胀的几个有用的辅助结果。
In this paper, we prove the Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture for unitary groups $U_n\times U_{n+1}$ in all the endoscopic cases. Our main technical innovation is the computation of the contributions of certain cuspidal data, called $*$-generic, to the Jacquet-Rallis trace formula for linear groups. We offer two different computations of these contributions: one, based on truncation, is expressed in terms of regularized Rankin-Selberg periods of Eisenstein series and Flicker-Rallis intertwining periods. The other, built upon Zeta integrals, is expressed in terms of functionals on the Whittaker model. A direct proof of the equality between the two expressions is also given. Finally several useful auxiliary results about the spectral expansion of the Jacquet-Rallis trace formula are provided.
